Improving the robustness of the immersed interface method through regularized velocity reconstruction.

The growing interest in blimp technology underscores the need for dynamic models that capture their flight behavior and improve control strategies. This paper presents, for the first time, a unified analysis of the aeroelastic stability and control of fully flexible blimps. The hull and fins are modeled as Euler–Bernoulli beams with free–free and fixed–free boundary conditions, respectively. Equations of motion are derived in the body frame using the Euler–Lagrange approach, incorporating hull added-mass effects and aerodynamic forces on the hull and fins. A perturbation approach divides the problem into a zeroth-order rigid-body dynamics for steady-level flight and a linearized first-order aeroelastic model. The zeroth-order solution supplies constant inputs to the first-order problem, which is then applied to the Skyship-500 with standard and thin-skin designs. Stability analysis confirms the model against prior work and identifies hump-mode flutter as the dominant instability. For thin-skinned blimps, this occurs at low forward speeds, while soft flutter emerges at higher speeds. To address maneuverability during hump-mode flutter, a linear quadratic regulator is applied. Results show that control inputs for a fully flexible blimp differ substantially from those of rigid or partially elastic models, emphasizing the importance of accounting for fin elasticity.

The stability and dynamics of flows past axisymmetric bubble-shaped rigid bluff bodies have been numerically and experimentally investigated. Motivated by the shapes of bubbles rising in quiescent liquids the bluff bodies were modelled as spherical and elliptical caps. The geometries are characterised by their aspect ratio, $\chi$ , defined as the ratio of the height of the bubble to the base radius, which is varied from $0.2$ to $2.0$ . Linear stability analyses were carried out on axisymmetric base flow fields subject to three-dimensional perturbations. As observed in earlier studies on bluff-body wakes, the primary bifurcation is stationary, followed by an oscillatory secondary bifurcation, with the leading global mode corresponding to azimuthal wavenumber $m = 1$ . The domain of stability is found to increase with aspect ratio for both of the geometries considered in the present study. The critical Reynolds number corresponding to the primary bifurcation is found to be independent of the aspect ratio when re-scaled using the extent of the recirculation region and the maximum of the reverse-flow velocity as the length and velocity scales, respectively. The wake flow features were characterised experimentally using laser-induced fluorescence and particle-image-velocimetry techniques. It is observed that the flow has a planar symmetry following the primary bifurcation, which is retained beyond the secondary bifurcation. The experimentally measured wavelengths and frequencies are in excellent agreement with the results obtained from global stability analyses. These observations were further corroborated using direct numerical simulations of the three-dimensional flow field. The critical Reynolds numbers corresponding to both primary and secondary bifurcations, and the dominant modes obtained using proper orthogonal decomposition of the experimentally measured velocity fields, are found to agree well with the global mode shapes and numerically computed flow fields.

To analyze the dynamic coupling mechanisms between the nonlinear motion of a helicopter's bluff-body slung load and its unsteady aerodynamic load, and to further improve the prediction accuracy of coupling effects during the helicopter' slung load operations, this paper establishes the numerical simulation method based on computational fluid dynamics (CFD), which is applicable to the bluff-body slung load. Then, the mathematical model of the sling constraining the motion of the slung load is developed, and its rigid-body dynamics model of the slung load is also established. By coupling the CFD model of the slung load with the six-degree-of-freedom rigid-body dynamics model, the dynamic coupling mechanisms between the nonlinear motion of the bluff-body slung load and its unsteady aerodynamic loads are analyzed. The paper clarifies the influence of the transition from narrow-side to broad-side orientations of the slung load on the aerodynamic motion coupling characteristics. The analysis results indicate that the transition, which is triggered by the continuous increase in yaw angle oscillation amplitude, is the primary cause of instability during high-speed flight. During the transition, the drag, the side force and the roll and pitch moments of the slung load rapidly exchange and redistribute. This leads to the rapid attenuation of longitudinal oscillation, while the lateral oscillation amplitude increases significantly. Simultaneously, the yaw angle enters into a stable "spinning" mode. When the speed increases from 40 km/h to 64 km/h, the instability time occurs 40% earlier, and the oscillation amplitude increases by 150%.

A variety of Offshore Floating Photovoltaics (OFPVs) applications rely on the capacity of their floating support structures displacing in the shape of surface waves to reduce extreme wave-induced loads exerted on their floating-mooring system. This wave-adaptive displacement behaviour is typically realized through two principal design approaches, either by employing slender and continuously deformable structures composed of highly elastic materials or by decomposing the structure into multiple floating rigid pontoons interconnected via flexible connectors. The hydrodynamic behaviour of these structures is commonly analyzed in the literature using potential flow theory, to characterize wave loading, whereas in order to deploy such OFPV prototypes in realistic marine environments, a high-fidelity numerical fluid–structure interaction model is required. Thus, a versatile three-dimensional numerical scheme is herein presented that is capable of handling non-linear fluid-flexible structure interactions for Very Flexible Floating Structures (VFFSs): Multibody Dynamics (MBD) for modularized floating structures and floating-mooring line interactions. In the present study, this is achieved by employing the Smoothed Particles Hydrodynamics (SPH) fluid model of DualSPHysics, coupled both with the MBD module of Project Chrono and the MoorDyn+ lumped-mass mooring model. The SPH-MBD coupling enables modelling of large and geometrically non-linear displacements of VFFS within an Applied Element Method (AEM) plate formulation, as well as rigid body dynamics of modularized configurations. Meanwhile, the SPH-MoorDyn+ captures the fully coupled three-dimensional response of floating-mooring and floating-floating dynamics, as it is employed to model both moorings and flexible interconnectors between bodies. The coupled SPH-based numerical scheme is herein validated against physical experiments, capturing the hydroelastic response of VFFS, rigid body hydrodynamics, mooring line dynamics, and flexible connector behaviour under wave loading. The demonstrated numerical methodology represents the first validated Computational Fluid Dynamics (CFD) application of moored VFFS in three-dimensional domains, while its robustness is further confirmed using modular floating systems, enabling OFPV engineers to comparatively assess these two types of wave-adaptive designs in a unified numerical framework.

Morphing technology can potentially improve the aerodynamic and flight performance of aircraft. A flexible trailing edge structure with corrugated panels is one of the promising candidates for camber morphing. While the aerodynamic advantages of the morphing concept have been proved, its performance in flight control situations remains to be investigated. This study develops a multidisciplinary simulation framework for aircraft with morphing control surfaces, combining the finite element method, unsteady vortex lattice method, rigid-body flight dynamics, and the linear quadratic integration controller. Flight maneuvers in pitch rate are simulated for morphing aircraft with different structural designs and flight conditions. The results demonstrate that control performance by morphing can be degraded due to the aeroelastic behavior of morphing control surfaces, and this phenomenon can be predicted by the proposed design index.

Waist assistive exoskeleton is a wearable robot used to alleviate muscle fatigue and prevent lower back injury for workers during repetitive load lifting. Multi-joint human-robot coupling, the effect of human control and the model uncertainties like load variations make the robust controller design of waist assistive exoskeleton become challenged. Most existed control methods are based on a simplified dynamic model and neglect model uncertainties, which leads to a limited control performance. This paper focuses on the dynamic modeling and high-performance force control of waist assistive exoskeleton. In order to obtain a dynamic model which is accurate as well as suitable for controller design, a 5-DOF human-robot rigid body dynamics is established first. Then holonomic constraints are proposed to describe the control effect of the wearer, which helps convert the 5-DOF dynamics into a 1-DOF dynamics. Based on the established 1-DOF dynamics, adaptive robust force control strategy is proposed to effectively address various model uncertainties and disturbances. Comparative simulations and experiments indicate that the proposed control method can realize accurate and robust force control performance under different loads.

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.

We propose a novel numerical test to evaluate the reliability of numerical propagations, leveraging the fiber bundle structure of phase space typically induced by Lie symmetries, though not exclusively. This geometric test simultaneously verifies two properties: (i) preservation of conservation principles, and (ii) faithfulness to the symmetry-induced fiber bundle structure. To generalize the approach to systems lacking inherent symmetries, we construct an associated collective system endowed with an artificial G-symmetry. The original system then emerges as the G-reduced version of this collective system. By integrating the collective system and monitoring G-fiber bundle conservation, our test quantifies numerical precision loss and detects geometric structure violations more effectively than classical integral-based checks. Numerical experiments demonstrate the superior performance of this method, particularly in long-term simulations of rigid body dynamics and perturbed Keplerian systems.

Abstract The moist shallow‐water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as “physics–dynamics coupling”. Without moist physics, the traditional shallow‐water equations are a simplified form of the atmospheric equations of motion and so are computationally cheap but retain many relevant dynamical features of the atmosphere. Introducing physics into the shallow‐water model in the form of moisture provides a tool to experiment with numerical techniques for physics–dynamics coupling in a simple dynamical model. In this article, we compare some of the different moist shallow‐water models by writing them in a general formulation. The general formulation encompasses three existing forms of the moist shallow‐water equations and also a fourth, previously unexplored formulation. The equations are coupled to a three‐state moist physics scheme that interacts with the resolved flow through source terms and produces two‐way physics–dynamics feedback. We present a new compatible finite‐element discretisation of the equations and apply it to the different formulations of the moist shallow‐water equations in three test cases. The results show that the models capture generation of cloud and rain and physics–dynamics interactions, and demonstrate some differences between moist shallow‐water formulations and the implications of these different modelling choices.

Abstract This tribute to Hermann Haken, the great theoretical physicist, explores the idea—based on a reconsideration of the experiments that led to the HKB model—that intentions (an emergent ‘mental force’) are hidden~exposed in order parameter fluctuations that arise due to special boundary conditions or rate-independent constraints on the basic coordination dynamics of human brain and behavior.

The strong interlayer coupling in black phosphorus (BP), arising from wavefunction overlap between layers, is critical for understanding its electronic and optical properties. Here, we utilize terahertz (THz) spectroscopy to study phonon dynamics in BP. We identify two peaks at 6 and 8.5 meV in steady-state THz spectra, which are attributed to low-frequency interlayer phonon modes. Both modes exhibit anharmonic phonon coupling behavior below 150K, manifesting as temperature-dependent red shifts. Using time-resolved THz spectroscopy, we observe significantly increased THz absorption under photoexcitation, arising from the transient enhancements of the extended Drude component and the oscillator strengths of interlayer phonons in non-equilibrium. These findings highlight the critical role of interlayer phonon dynamics in understanding many-body physics in BP.

Collective migration of epithelial cells drives diverse tissue remodeling processes. In many cases, a free tissue edge polarizes the cells to promote directed motion, but how edge-free or closed epithelia initiate migration remains unclear. Here, we show that the rotational migration of follicular epithelial cells in the Drosophila egg chamber is a self-organizing process. Combining experiments and theoretical modeling, we identify a positive feedback loop in which the mechanosensitive behavior of the atypical cadherin Fat2 synergizes with the rigid-body dynamics of the egg chamber to both initiate and sustain rotation. Mechanical constraints arising from cell–cell interactions and tissue geometry further align this motion around the egg chamber’s anterior–posterior axis. Our findings reveal a biophysical mechanism — combining Fat2-mediated velocity–polarity alignment, rigid-body dynamics, and tissue geometry — by which a closed epithelial tissue self-organizes into persistent, large-scale rotational migration in vivo, expanding current flocking theories.

Rigid body dynamics traditional assumes no deformation under external forces, yet materials exhibit elastic and thermal effects that significantly influence stress and strain distributions. This study develops a couple thermoelastic framework to investigate how thermal and elastic terms affect the dynamic response of rigid bodies. The governing partial differential equations were derived by integrating principles from continuum mechanics, thermodynamics, and rigid body motion. Analytical example of a heated plate subjected to thermal gradients and external forces, was solved to demonstrate the model’s predictive capability. The result shows that constrained thermal expansion generates significant stresses, while elasticity governs deformation recovery and structural stability. The interaction of these effects shapes displacement fields,alters stress distributions, and impact vibration behaviour under dynamic loading. These findings provide insights into the performance of materials and structures exposed to fluctuating mechanical and thermal conditions, particularly in aerospace, mechanical, and structural engineering applications. The proposed model offers a unified theoretical framework for predicting thermoelastic effects in rigid bodies and supports the design of safer and more durable components. Future research may extend the approach to nonlinear and transient conditions for enhanced predictive accuracy.

The study of wave impact structures is a key focus of coastal protection and marine hazard mitigation. Fluid–structure coupling numerical simulation is a powerful technical method. This paper presents an integrated numerical framework combining the non-hydrostatic method with the immersed boundary method to investigate wave–structure interactions. The framework incorporates rigid body dynamics and a collision detection algorithm to resolve coupled hydrodynamic and structural interactions under wave force. A novel water elevation correction method with adaptive flux constraints at wave–structure interfaces successfully addresses mass conservation challenges during wave propagation over obstacles. Model validation through submerged bar benchmark tests demonstrates the accuracy of numerical model in wave propagation simulation. Combined wave flume experiments and parametric studies further validate the model in simulating coastal processes spanning wave generation, run-up dynamics, and structural responses. Comparative analysis reveals that simulated motion trajectories achieve good agreement with experimental measurements, particularly in capturing the effects of nonlinear wave–structure coupling. Numerical results of surge wave impacts on structures demonstrate shelter structures can reduce the impact forces by 50%, with system-scale analysis revealing stabilized force attenuation of approximately 15% under increasing structural density. An attenuation coefficient analysis quantifies the relationship between the number of sheltering structures and the reduction in wave force.

Firearm-related injuries, particularly those involving the cranio-cervical region, pose significant challenges in forensic pathology due to the anatomical complexity and the concentration of vital structures. This case report describes a fatal hunting accident involving a close-range shot with a large-caliber slug bullet, resulting in a high-energy transfer wound with an atypical exit site on the right side of the neck. Autopsy findings, supported by digital imaging, revealed deviation of the projectile's trajectory due to impact with the C6 vertebral body, consistent with bullet destabilization and subsequent overturning. The atypical morphology of the exit wound-initially suggestive of soot deposition or thermal alteration-was reinterpreted as a postmortem dehydration artifact, linked to prolonged refrigeration or freezing in the mortuary. Notably, other wounds covered by clothing did not exhibit similar changes, suggesting a role of postmortem environmental exposure in modifying wound appearance. Reconstruction of the ballistic event required a multidisciplinary approach integrating wound ballistics, rigid body dynamics, postmortem artifact analysis, and garment lesion evaluation. Although limitations in textile analysis precluded definitive conclusions regarding garment damage interpretation, the overall trajectory analysis strongly supported a left-to-right bullet path. This case highlights the critical importance of interdisciplinary collaboration in the forensic reconstruction of complex firearm injuries and underscores the potential for interpretive error when postmortem changes and ballistic deviations are not fully considered. The application of falsifiability criteria further strengthens the proposed reconstruction and excludes alternative hypotheses lacking empirical support.

Botulinum neurotoxin (BoNT) is an intensely toxic substance produced by Clostridium botulinum causes neuroparalytic syndrome botulism. In the present study, twelve sialic acid analogues are modeled at the binding pocket of BoNT/B to investigate the carbohydrate recognition using rigid body dynamics. Among the twelve analogues modeled 4-O-acetyl sialic acid and Amide sialic acid exhibits highest inhibitory potency towards BoNT/B. Molecular dynamics shows that direct and water-mediated hydrogen bonds stabilize BoNT/Bsialic acid complexes. An analysis of the interactions and energy calculations reveals that 4-O-acetyl sialic acid has enhanced affinity which can be effectively used to design the glycan-based inhibitor for botulism.

We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. To ensure constraint satisfaction, we use an implicit integration scheme. For this purpose, we derive compatible dynamic equations expressed through the quaternion time derivative, adopting an additive approach to quaternion updates instead of a multiplicative one, while enforcing quaternion unit-length as a constraint. We support all joints between rigid bodies that restrict subsets of the three translational or three rotational degrees of freedom, including position- and force-based actuation. Their constraints are formulated such that Lagrange multipliers are interpretable as joint forces and torques. We discuss a unified solution strategy for systems with redundant constraints, overactuation, and passive degrees of freedom, by eliminating redundant constraints and navigating the subspaces spanned by multipliers. As our method uses a standard additive update, we can interface with unconditionally-stable implicit integrators. Moreover, the simulation can readily be made differentiable as we show with examples.

We propose the formulation of forward and differentiable rigid-body dynamics using Lie-algebra rotation derivatives. In particular, we show how this approach can easily be applied to incremental-potential formulations of forward dymamics, and we introduce a novel definition of adjoints for differentiable dynamics. In contrast to other parameterizations of rotations (notably the popular rotation-vector parameterization), our approach leads to painlessly simple and compact derivatives, better conditioning, and higher runtime efficiency. We demonstrate our approach on fundamental rigid-body problems, but also on Cosserat rods as an example of multi-rigid-body dynamics.

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.